The ground state of a system of particles interacting through short ranged central potentials is a triangular lattice arrangement [1]}. The introduction of disorder can lead to fluctuations in the positions, and consequently elastic properties such as the local shear modulus [2]}, [3]}.
Many studies have considered the effect of small disorder about the crystalline state, whose periodicity facilitates an exact theoretical treatment of their properties. However, when disorder is introduced into an athermal system, such as in amorphous configurations, developing theories that predict macroscopic properties becomes challenging  [4]}, [5]}, [6]}.
In such crystals, the contribution of lattice phonons is suppressed, and crystallization results from energy minimization, and they exhibit properties of athermal materials.
Many examples of such disordered near-crystalline systems exist including glasses with high crystalline order [7]}, [8]}, [9]}, polycrystals [10]}, [11]} as well as colloidal crystals [12]}.
In such systems, the changes in the interparticle potentials introduced through quenched disorder affects their large scale properties when force balance conditions are exactly imposed, leading to amorphous structures. This leads to elastic heterogeneity at the microscopic scale, and therefore continuum elasticity frameworks are inapplicable in such materials.
